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Finding the Third Proportional to 413,226 and 584,910

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Solution

The third proportional to 413,226 and 584,910 is: 827,923.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    413,226 : 584,910 = 584,910 : x
  2. Step 2: Convert to fraction form
    413,226/584,910 = 584,910/x
  3. Step 3: Cross multiply
    413,226x = 584,910 × 584,910
  4. Step 4: Simplify right side
    413,226x = 342,119,708,100
  5. Step 5: Solve for x
    x = 342,119,708,100/413,226
  6. Step 6: Final answer
    x = 827,923.96

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.